Michael C. Burkhart

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math.GR2025

Actions of nilpotent groups on nilpotent groups

Michael C. Burkhart

For finite nilpotent groups $J$ and $N$ , suppose $J$ acts on $N$ via automorphisms. We exhibit a decomposition of the first cohomology set in terms of the first cohomologies of the…

math.GR2025

Conjugacy conditions for supersoluble complements of an abelian base and a fixed point result for non-coprime actions

Michael C. Burkhart

We demonstrate that two supersoluble complements of an abelian base in a finite split extension are conjugate if and only if, for each prime $p$ , a Sylow $p$ -subgroup of one comple…